Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On multivariate Lagrange interpolation

Authors: Thomas Sauer and Yuan Xu
Journal: Math. Comp. 64 (1995), 1147-1170
MSC: Primary 41A63; Secondary 41A05, 65D05
MathSciNet review: 1297477
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formula for Lagrange interpolation of degree n of a function f, which is a sum of integrals of certain $(n + 1)$st directional derivatives of f multiplied by simplex spline functions. We also provide two algorithms for the computation of Lagrange interpolants which use only addition, scalar multiplication, and point evaluation of polynomials.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 41A63, 41A05, 65D05

Retrieve articles in all journals with MSC: 41A63, 41A05, 65D05

Additional Information

Keywords: Lagrange interpolation, finite difference, simplex spline, remainder formula, algorithm
Article copyright: © Copyright 1995 American Mathematical Society